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A matrix D'Alembert formula for coupled wave initial value problems

✍ Scribed by L. Jódar; D. Goberna

Book ID
104353288
Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
710 KB
Volume
35
Category
Article
ISSN
0898-1221

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✦ Synopsis

If c is an invertible matrix in C rxr, the coupled wave equation initial value problem

, and ut(x, 0) = g(x) for -co < z < co is studied. A matrix D'Alembert formula for the closed form solution of the coupled wave equation is given. The approach is based on the Fourier transform, the holomorphic matrix functional calculus and some elements of complex variable functions. For the scalar case, the proposed D'Alembert formula coincides with the classical one.

📜 SIMILAR VOLUMES

The Global Attractors for the Periodic I
The Global Attractors for the Periodic Initial Value Problem For a Coupled Non-linear Wave Equation
✍ Guo Boling; Yang Linge 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 451 KB 👁 2 views

The existence of global attractors of the periodic initial value problem for a coupled non-linear wave equation is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of uniform a priori estimates for time.